No US gold coins were minted in 1975. Proof sets contained only the standard circulating coins of the time: A 1975 dated cent, nickel, and dime, and a dual-dated 1776-1976 Bicentennial quarter, half dollar, and dollar.
There were no British 1998 10 Pence coins minted for circulation. There were some minted for Proof and Mint uncirculated coin sets.
There were 1 Rand and 2 Rand coins minted in gold in 1975, and some were produced for proof sets. South Africa in 1975 sold three different proof sets: an 8-coin set (1/2 cent, 1 cent, 2 cents, 5 cents, 10 cents, 20 cents, 50 cent and 1 rand [silver]); a 2-coin set (the two gold coins); and a 10-coin set (all of the above). I would suggest looking on eBay (the KM numbers are KM#63 for the 1 Rand and KM#64 for the 2 Rand).
It is extremely unlikely that a 2000 general circulation coin would be minted in 2001. It is not so unlikely that some bullion Proof coins might be minted in the year after the date indicated on the coin.
The only Australian coins minted for general circulation in 2007 were the 5, 10 and 20 cent coins and the 2 Dollar coin. The 50 cent coin was only minted as a Non-Circulating Commemorative and, the 1 Dollar coin was only minted for Uncirculated or Mint year sets and Proof sets.
Such a coin does not exist. The only British Half-Sovereign coins minted in 1923 were minted at the Pretoria Mint in South Africa and were all Proof coins.
For coins minted in British India (pre-1947), the Bombay minted used a dot. For coins minted in independent India, (post-1947), the Bombay mint uses a small diamond (although proof coins from 1969 to 1995 used a "B").
No, a proof coin does not have to be minted in San Francisco. Proof coins can be minted at any official United States Mint facility. The San Francisco Mint is one of the facilities that produces proof coins, but there are others as well, such as the Philadelphia and West Point Mints.
A normal coin is what is released into circulation. A Proof coin is one that has been struck on specially prepared and polished dies and hand polished to give a mirror like finish. Proof coins can be minted in the same metals as normal coins, but quite often, they are minted in precious metals. Proof coins are not intended for circulation, but for investors and serious collectors and they are usually packaged for protection and sold in their year of minting for a price much greater than the face value of the coin.
The U.S. Mint was not issuing gold coins in 1975.
A "Proof" or "Proof - Fleur Du Coin" coin is one that is struck on specially prepared and highly polished dies. After the coin is struck, it is hand polished to give a mirror like finish. Most modern "Proof" coins have the highlights frosted to give a good contrast. "Proof" coins are made from the same metal as general circulation coins, but are often also made from silver or gold. "Proof" coins are worth a good deal more than their face value and are intended as a souvenir or investment.
There were only two years when an Australian Crown (Five Shilling) coins was minted, being 1937 and 1938. If by "polished die" you mean a "Proof" coin, both the 1937 and 1938 coins were minted as Proof and general circulation coins.
The Constitution coins were minted to commemorate the 200th Anniversary of the United States Constitution. Four different coins were minted: proof and uncirculated dollars; and proof and uncirculated $5 gold coins, but they were not made in 1787, they were struck in 1987. Post new question as to which type?